I wish I knew more about the motivation and process of the artist behind it. My guess is that the wavy, sinusoidal legs were a result of simple curiosity - wrapping a strip of material around the rim of a bowl and seeing what resulted.

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Or, only slightly less likely, the designer may have been an architect who recalled the fascinating structural properties of developable surfaces.

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Either way, while surely there's a way to replicate this serendipitous process in CAD, my mind generally turns to finding a mathematical formulation for my base shapes. The whole reason I'm in 3D printing is because I'm allergic to manual form-finding! It allows me to do stuff like this:

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XX - grasshopper video - iterating over # of humps. What takes my software seconds would take me hours.

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In this case, I saw two roads ahead. The first would be to simply create my own developable surface and walk away. But I recalled a more intriguing possibility, what a scientist might call an 'analytical solution'. 

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That solution is called the enneper surface. It's a mathematical object with several special properties, among them myriad rotational symmetries. Put more artfully, they can resemble a wavy-petaled flower like an iris. 

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Enneper surfaces are generally defined with three 'petals', although an infinite number are possible. After moving my slider around, as shown above, I settled on the four petal arrangement. 

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Next, I adapted the equation to give me control over its spatial properties - the height, depth, amount of curl, and so forth. 

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This done, I turned my attention to the bowl within. A solid shape seemed the best solution initially, but this I had to abandon as it was drowned out by the loudness of the base. Not enough harmony. 

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While painting the bowl with a bright color or aleatory pattern might have solved this dilemma, I wanted all pieces in my Living Room Collection to have the same color, a gentle ivory. 

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This meant that visual weight would have to come from the texture of the bowl itself, which meant weaving. My first thought was to use an octagonal weave, common in both parametric design software and the baskets of Native Peoples. 

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But that would have tilted the balance in the other direction, drowning out an already loud base. So I opted for the simple weave.

 

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Once in a great while, less is more (a simple weave)

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Next, I added height and poise to the walls of the base shape, beefed up the upper lip, pressed print, and came back four days later. 

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Just kidding. I had to pull all kinds of stunts to make the weave printable - the first incarnation weighed in at 1 GB, which is way more file than my software and printer can handle. But I put it on a diet and got things to work.

 

I find it funny that an object that can be described so concisely in the language of math (it only has four bits; the in and out vertical weave lines, and the in and out horizontal weave lines) becomes so verbose when translated into the language of my printer.

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